f(z)=(z-3)sein(1/(2+z))

For the Laurent series for about .
The convergence region is the disc with center in z=-2 and , since we have singularities in z=3 and z=-2.
Is this correct?
The textbook unswer is that the series converges for

For the Laurent series for about .
The convergence region is the disc with center in z=-2 and , since we have singularities in z=3 and z=-2.
Is this correct?
The textbook unswer is that the series converges for

Setting...

(1)

... You obtain...

(2)

... so that is...

(3)

The (3) converges everywhere is and has at z=-2 an essential singularity...